We also measured the temperature-dependent remnant magnetization which provides a convenient probe of the AFM transition in many iridates in virtue of the canted moment induced by octahedral rotation. The data in Figure 2(b) reveals a magnetic transition of the HSL at around 120 K, which is close to the transition temperature of the bilayer SL and much lower than the single-layer SL [1]}, [2]}. The size of the in-plane net moment per Ir site is however much bigger than that of the bilayer SL and about half of the single-layer SL [1]}. These results have a number of important implications. Firstly, it suggests that the magnetic ground state of the HSL is a canted AFM order. Secondly, the observed predominant in-plane canted moments and the small but finite out-of-plane canted moments require the AFM moments of at least one of the two slabs to have an in-plane component. If only one of them has planar moments, it is most likely to be the monolayer slab given its own reported XY-anisotropy [4]}, [5]}. In the other extreme, if both slabs have and only have planar moments, the canting angle and/or the averaged size of the local ordered moments would have to be considerably reduced from that of the single-layer SL, unless the two slabs have opposite canting directions. We ruled out the possibility of having opposite canting directions by magnetic hysteresis loop measurements of magnetoresistance and magnetization, both of which shown in Figure 2(c) and (d) exhibit a single coercivity field consistently. Last but not least, regardless of the anisotropy, a single AFM transition of the HSL would mean that both slabs are ordered simultaneously. In other words, since the inter-slab coupling is critical to the long-range order stability of such a quasi-2D system [1]}, [7]}, the monolayer slab in the HSL cannot order without the adjacent bilayer slabs being ordered as well, accounting for the observed transition temperature. In short, what is already clear from magnetometry is that the HSL is not just a simple superposition of the monolayer and bilayer.
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